Gaussian Process Models for Quantitative Finance
Description
This book describes the diverse applications of Gaussian Process (GP) models in mathematical finance. Spurred by the transformative influence of machine learning frameworks, the text aims to integrate GP modeling into the fabric of quantitative finance. The first half of the book provides an entry point for graduate students, established researchers and quant practitioners to get acquainted with GP methodology. A systematic and rigorous introduction to both GP fundamentals and most relevant advanced techniques is given, such as kernel choice, shape-constrained GPs, and GP gradients. The second half surveys the broad spectrum of GP applications that demonstrate their versatility and relevance in quantitative finance, including parametric option pricing, GP surrogates for optimal stopping, and GPs for yield and forward curve modeling. The book includes online supplementary materials in the form of half a dozen computational Python and R notebooks that provide the reader direct illustrations of the covered material and are available via a public GitHub repository.
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Persons
Mike Ludkovski is a Professor of Statistics and Applied Probability at University of California Santa Barbara. He was Department Chair during 2018-2022 and since 2016 is a Co-Director of the Center for Financial Mathematics and Actuarial Research. He has 15+ years of experience and 80+ publications in stochastic modeling of energy markets, numerical methods for stochastic control and predictive analytics. Among his current research interests are Monte Carlo techniques for optimal stopping/stochastic control, non-zero-sum stochastic games, and applications of machine learning in longevity and non-life insurance. He serves on 5+ Editorial Boards and his research has been funded by NSF, ARPA-E and Society of Actuaries. During 2015-2016 he was Chair of the SIAM Activity Group on Financial Mathematics & Engineering. He co-edited the volume on "Commodities, Energy and Environmental Finance" (2015). Ludkovski holds a Ph.D. in Operations Research and Financial Engineering from Princeton University and has held visiting positions at London School of Economics and Paris Dauphine University.
Jimmy Risk is an Assistant Professor of Mathematics and Statistics at California Polytechnic State University Pomona. He was temporary chair during Summer 2022 and has advised nine master's thesis students since taking his position in Fall 2017, several of which involving applications of Gaussian processes in modern data science including neural networks, natural language processing, and super-resolution. His education involves a Ph.D. in Statistics and Applied Probability with an emphasis in Financial Mathematics from University of California Santa Barbara, which has driven publications involving pricing and tail risk analysis using Gaussian processes to approximate conditional expectations. Additionally, Risk has an extensive actuarial science background, including developing a Gaussian process model for mortality rates, and more recently winning an open international mortality prediction contest held by the Society of Actuaries alongside Mike Ludkovski. Risk's recent research interests involve the theory and applications of Gaussian process kernels, which lie in the Reproducing Kernel Hilbert Space framework.
Content
- 1. Gaussian Process Preliminaries.- 2. Covariance Kernels.- 3. Advanced GP Modeling Topics.- 4. Option Pricing and Sensitivities.- 5. Optimal Stopping.- 6. Non-Parametric Modeling of Financial Structures.- 7. Stochastic Control.